Genus 2 Curves Database Igusa CM Invariants Database Quartic CM Fields Database

A quartic CM field field K is represented by invariants [D,A,B], where K = Q[x]/(x4+Ax2+B), and D is the discriminant of the totally real quadratic subfield (hence A2-4B = m2D for some m).

Class number: [Non-normal] [Cyclic]

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
[25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48]
[49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72]
[73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96]
[97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120]
[121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] [134] [135] [136] [137] [138] [139] [140] [141] [142] [143] [144]
[145] [146] [147] [148] [149] [150] [151] [152] [153] [154] [155] [156] [157] [158] [159] [160] [161] [162] [163] [164] [165] [166] [167] [168]
[169] [170] [171] [172] [173] [174] [175] [176] [177] [178] [179] [180] [181] [182] [183] [184] [185] [186] [187] [188] [189] [190] [191] [192]
[193] [194] [195] [196] [197] [198] [199] [200] [201] [202] [203] [204] [205] [206] [207] [208] [209] [210] [211] [212] [213] [214] [215] [216]
[217] [218] [219] [220] [221] [222] [223] [224] [225] [226] [227] [228] [229] [230] [231] [232] [233] [234] [235] [236] [237] [238] [239] [240]
[241] [242] [243] [244] [245] [246] [247] [248] [249] [250] [251] [252] [253] [254] [255] [256] [257] [258] [259] [260] [261] [262] [263] [264]
[265] [266] [267] [268] [269] [270] [271] [272] [273] [274] [275] [276] [277] [278] [279] [280] [281] [282] [283] [284] [285] [286] [287] [288]
[289] [290] [291] [292] [293] [294] [295] [296] [297] [298] [299] [300] [301] [302] [303] [304] [305] [306] [307] [308] [309] [310] [311] [312]
[313] [314] [315] [316] [317] [318] [319] [320] [321] [322] [323] [324] [325] [326] [327] [328] [329] [330] [331] [332] [333] [334] [335] [336]
[337] [338] [339] [340] [341] [342] [343] [344] [345] [346] [347] [348] [349] [350] [351] [352] [353] [354] [355] [356] [357] [358] [359] [360]
[361] [362] [363] [364] [365] [366] [367] [368] [369] [370] [371] [372] [373] [374] [375] [376] [377] [378] [379] [380] [381] [382] [383] [384]
[385] [386] [387] [388] [389] [390] [391] [392] [393] [394] [395] [396] [397] [398] [399] [400] [401] [402] [403] [404] [405] [406] [407] [408]
[409] [410] [411] [412] [413] [414] [415] [416] [417] [418] [419] [420] [421] [422] [423] [424] [425] [426] [427] [428] [429] [430] [431] [432]
[433] [434] [435] [436] [437] [438] [439] [440] [441] [442] [443] [444] [445] [446] [447] [448] [449] [450] [451] [452] [453] [454] [455] [456]
[457] [458] [459] [460] [461] [462] [463] [464] [465] [466] [467] [468] [469] [470] [471] [472] [473] [474] [475] [476] [477] [478] [479] [480]
[481] [482] [483] [484] [485] [486] [487] [488] [489] [490] [491] [492] [493] [494] [495] [496] [497] [498] [499] [500] [501] [502] [503] [504]
[505] [506] [507] [508] [509] [510] [511] [512] [513] [514] [515] [516] [517] [518] [519] [520] [521] [522] [523] [524] [525] [526] [527] [528]
[529] [530] [531] [532] [533] [534] [535] [536] [537] [538] [539] [540] [541] [542] [543] [544] [545] [546] [547] [548] [549] [550] [551] [552]
[553] [554] [555] [556] [557] [558] [559] [560] [561] [562] [563] [564] [565] [566] [567] [568] [569] [570] [571] [572] [573] [574] [575] [576]

Class group C3 x C147 non-normal (D4) quartic CM field invariants: 139 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 9281, 21242629] C3 x C147 ---) [21242629, 6357, 4792205] C3 x C1911
2) [5, 5737, 8008841] C3 x C147 138) [8008841, 3779, 1568000] C3 x C147
3) [5, 9781, 23812589] C3 x C147 139) [23812589, 7697, 8857805] C3 x C147
4) [73, 6630, 6205097] C3 x C147 ---) [6205097, 3315, 1196032] C21 x C147
5) [89, 5414, 6638633] C3 x C147 136) [6638633, 2707, 172304] C3 x C147
6) [137, 6310, 6788777] C3 x C147 137) [6788777, 3155, 791312] C3 x C147
7) [229, 401, 33273] C3 x C147 ---) [3697, 802, 27709] C147
8) [229, 710, 67401] C3 x C147 ---) [7489, 355, 14656] C147
9) [229, 2198, 1174825] C3 x C147 ---) [46993, 1099, 8244] C147
10) [257, 854, 116537] C3 x C147 ---) [116537, 427, 16448] C147
11) [257, 1022, 224113] C3 x C147 ---) [224113, 511, 9252] C147
12) [277, 873, 188801] C3 x C147 106) [188801, 1746, 6925] C3 x C147
13) [521, 2255, 192656] C3 x C147 ---) [12041, 1391, 408464] C3 x C735
14) [733, 994, 173709] C3 x C147 ---) [19301, 497, 18325] C147
15) [733, 437, 46093] C3 x C147 ---) [46093, 874, 6597] C147
16) [761, 859, 129488] C3 x C147 ---) [8093, 1718, 219929] C147
17) [773, 625, 95917] C3 x C147 ---) [95917, 1250, 6957] C3 x C3 x C441
18) [977, 1886, 873617] C3 x C147 120) [873617, 943, 3908] C3 x C147
19) [1061, 1114, 272053] C3 x C147 108) [272053, 557, 9549] C3 x C147
20) [1373, 314, 19157] C3 x C147 ---) [19157, 157, 1373] C147
21) [1901, 1310, 155281] C3 x C147 ---) [3169, 655, 68436] C147
22) [2161, 1979, 239508] C3 x C147 60) [6653, 3833, 1143169] C3 x C147
23) [2213, 857, 116669] C3 x C147 ---) [2381, 1714, 267773] C147
24) [2213, 2497, 4673] C3 x C147 ---) [4673, 2071, 1071092] C147
25) [2281, 646, 67833] C3 x C147 ---) [7537, 323, 9124] C3 x C3 x C147
26) [2357, 2694, 1776697] C3 x C147 72) [10513, 1347, 9428] C3 x C147
27) [2557, 2541, 739037] C3 x C147 ---) [4373, 2581, 2557] C147
28) [2557, 881, 9297] C3 x C147 ---) [1033, 1762, 738973] C147
29) [2557, 4594, 5265981] C3 x C147 ---) [11941, 2297, 2557] C147
30) [2677, 893, 5949] C3 x C147 ---) [661, 1193, 216837] C147
31) [2713, 510, 21617] C3 x C147 ---) [21617, 255, 10852] C147
32) [2749, 1901, 61569] C3 x C147 61) [6841, 3802, 3367525] C3 x C147
33) [2917, 3837, 4493] C3 x C147 43) [4493, 2165, 352957] C3 x C147
34) [3221, 617, 87925] C3 x C147 ---) [3517, 1234, 28989] C147
35) [3221, 2954, 4133] C3 x C147 ---) [4133, 1477, 544349] C147
36) [3469, 1805, 85149] C3 x C147 68) [9461, 3610, 2917429] C3 x C147
37) [3469, 7005, 1963709] C3 x C147 86) [16229, 6625, 419749] C3 x C147
38) [3881, 6083, 1906900] C3 x C147 92) [19069, 6405, 3729641] C3 x C147
39) [4001, 1274, 5669] C3 x C147 ---) [5669, 637, 100025] C147
40) [4133, 1361, 7417] C3 x C147 62) [7417, 2722, 1822653] C3 x C147
41) [4481, 539, 44624] C3 x C147 ---) [2789, 1078, 112025] C147
42) [4493, 2562, 1191661] C3 x C147 ---) [3301, 1281, 112325] C147
43) [4493, 2165, 352957] C3 x C147 33) [2917, 3837, 4493] C3 x C147
44) [4493, 3153, 4093] C3 x C147 ---) [4093, 4453, 363933] C147
45) [4597, 2293, 210033] C3 x C147 ---) [2593, 3211, 165492] C147
46) [4597, 1345, 37377] C3 x C147 ---) [4153, 2690, 1659517] C147
47) [4729, 247, 4612] C3 x C147 ---) [1153, 494, 42561] C147
48) [4793, 5074, 5957069] C3 x C147 75) [11261, 2537, 119825] C3 x C147
49) [4793, 5266, 11597] C3 x C147 76) [11597, 2633, 1730273] C3 x C147
50) [4861, 8061, 14581253] C3 x C147 85) [15173, 5357, 1404829] C3 x C147
51) [4933, 257, 5413] C3 x C147 ---) [5413, 514, 44397] C147
52) [4937, 5443, 6635156] C3 x C147 81) [13709, 7049, 9128513] C3 x C147
53) [5081, 2251, 899648] C3 x C147 ---) [14057, 4502, 1468409] C147
54) [5153, 1303, 52148] C3 x C147 79) [13037, 2606, 1489217] C3 x C147
55) [5197, 7549, 12655269] C3 x C147 ---) [11621, 4021, 878293] C21 x C147
56) [5197, 2162, 149949] C3 x C147 ---) [16661, 1081, 254653] C3 x C3 x C147
57) [5741, 637, 88525] C3 x C147 ---) [3541, 1274, 51669] C147
58) [5741, 2433, 100597] C3 x C147 ---) [2053, 2529, 970229] C147
59) [6637, 2097, 1097693] C3 x C147 ---) [653, 1333, 325213] C147
60) [6653, 3833, 1143169] C3 x C147 22) [2161, 1979, 239508] C3 x C147
61) [6841, 3802, 3367525] C3 x C147 32) [2749, 1901, 61569] C3 x C147
62) [7417, 2722, 1822653] C3 x C147 40) [4133, 1361, 7417] C3 x C147
63) [7481, 4343, 2424356] C3 x C147 ---) [5009, 4339, 2992400] C147
64) [7537, 1171, 24372] C3 x C147 ---) [677, 2342, 1273753] C147
65) [8597, 1114, 757] C3 x C147 ---) [757, 557, 77373] C147
66) [8597, 817, 113141] C3 x C147 ---) [2309, 1634, 214925] C147
67) [8713, 1131, 213056] C3 x C147 ---) [3329, 2262, 426937] C147
68) [9461, 3610, 2917429] C3 x C147 36) [3469, 1805, 85149] C3 x C147
69) [9749, 890, 159029] C3 x C147 ---) [941, 445, 9749] C147
70) [10333, 953, 224469] C3 x C147 ---) [509, 1906, 10333] C147
71) [10457, 5263, 5771908] C3 x C147 ---) [4993, 5751, 7068932] C147
72) [10513, 1347, 9428] C3 x C147 26) [2357, 2694, 1776697] C3 x C147
73) [10949, 109, 233] C3 x C147 ---) [233, 218, 10949] C147
74) [11057, 1627, 194624] C3 x C147 ---) [3041, 3254, 1868633] C147
75) [11261, 2537, 119825] C3 x C147 48) [4793, 5074, 5957069] C3 x C147
76) [11597, 2633, 1730273] C3 x C147 49) [4793, 5266, 11597] C3 x C147
77) [12197, 125, 857] C3 x C147 ---) [857, 250, 12197] C147
78) [12821, 569, 809] C3 x C147 ---) [809, 1138, 320525] C147
79) [13037, 2606, 1489217] C3 x C147 54) [5153, 1303, 52148] C3 x C147
80) [13577, 2455, 9892] C3 x C147 ---) [2473, 4910, 5987457] C147
81) [13709, 7049, 9128513] C3 x C147 52) [4937, 5443, 6635156] C3 x C147
82) [14197, 909, 32657] C3 x C147 ---) [113, 979, 227152] C147
83) [14389, 4370, 4256221] C3 x C147 ---) [3109, 2185, 129501] C147
84) [15061, 1397, 182917] C3 x C147 ---) [3733, 2794, 1219941] C147
85) [15173, 5357, 1404829] C3 x C147 50) [4861, 8061, 14581253] C3 x C147
86) [16229, 6625, 419749] C3 x C147 37) [3469, 7005, 1963709] C3 x C147
87) [17929, 1658, 41797] C3 x C147 ---) [853, 829, 161361] C147
88) [18269, 821, 54329] C3 x C147 ---) [449, 1642, 456725] C147
89) [18661, 645, 99341] C3 x C147 ---) [821, 1290, 18661] C147
90) [18701, 3509, 2288153] C3 x C147 ---) [953, 3659, 1196864] C147
91) [18701, 1765, 213101] C3 x C147 ---) [4349, 3530, 2262821] C147
92) [19069, 6405, 3729641] C3 x C147 38) [3881, 6083, 1906900] C3 x C147
93) [19949, 2042, 324277] C3 x C147 ---) [613, 1021, 179541] C147
94) [23297, 503, 57428] C3 x C147 ---) [293, 1006, 23297] C147
95) [23917, 2178, 1090253] C3 x C147 ---) [293, 1089, 23917] C147
96) [24281, 1555, 598436] C3 x C147 ---) [89, 811, 97124] C147
97) [34253, 2354, 152221] C3 x C147 ---) [181, 1177, 308277] C147
98) [34253, 1518, 28033] C3 x C147 ---) [97, 759, 137012] C147
99) [42709, 1473, 275501] C3 x C147 ---) [149, 2705, 42709] C147
100) [45841, 407, 29952] C3 x C147 ---) [13, 733, 45841] C147
101) [54469, 325, 12789] C3 x C147 ---) [29, 650, 54469] C147
102) [55661, 1274, 183125] C3 x C147 ---) [293, 637, 55661] C147
103) [64373, 349, 14357] C3 x C147 ---) [293, 698, 64373] C147
104) [153949, 457, 13725] C3 x C147 ---) [61, 914, 153949] C49
105) [169313, 575, 40328] C3 x C147 ---) [8, 1150, 169313] C147
106) [188801, 1746, 6925] C3 x C147 12) [277, 873, 188801] C3 x C147
107) [225257, 3838, 78449] C3 x C147 ---) [1601, 1919, 901028] C21 x C147
108) [272053, 557, 9549] C3 x C147 19) [1061, 1114, 272053] C3 x C147
109) [281989, 2146, 23373] C3 x C147 ---) [53, 1073, 281989] C147
110) [312161, 719, 51200] C3 x C147 ---) [8, 1438, 312161] C147
111) [370561, 831, 80000] C3 x C147 ---) [8, 1662, 370561] C147
112) [386129, 677, 18050] C3 x C147 ---) [8, 1354, 386129] C147
113) [418721, 687, 13312] C3 x C147 ---) [13, 1374, 418721] C147
114) [539113, 1843, 714384] C3 x C147 ---) [41, 3686, 539113] C147
115) [552473, 915, 71188] C3 x C147 ---) [13, 1830, 552473] C147
116) [632257, 823, 11268] C3 x C147 ---) [313, 1646, 632257] C147
117) [691553, 845, 5618] C3 x C147 ---) [8, 1690, 691553] C147
118) [732533, 861, 2197] C3 x C147 ---) [13, 1722, 732533] C147
119) [787517, 1001, 53621] C3 x C147 ---) [29, 2002, 787517] C147
120) [873617, 943, 3908] C3 x C147 18) [977, 1886, 873617] C3 x C147
121) [881953, 967, 13284] C3 x C147 ---) [41, 1934, 881953] C147
122) [949937, 991, 8036] C3 x C147 ---) [41, 1982, 949937] C147
123) [1049569, 1039, 7488] C3 x C147 ---) [13, 2078, 1049569] C147
124) [1157701, 1461, 244205] C3 x C147 ---) [5, 2173, 1157701] C147
125) [1182421, 1117, 16317] C3 x C147 ---) [37, 2234, 1182421] C147
126) [1248217, 1147, 16848] C3 x C147 ---) [13, 2294, 1248217] C147
127) [1347341, 1169, 4805] C3 x C147 ---) [5, 2338, 1347341] C147
128) [1356409, 1547, 259200] C3 x C147 ---) [8, 3094, 1356409] C147
129) [1868057, 1403, 25088] C3 x C147 ---) [8, 2806, 1868057] C147
130) [2364409, 1547, 7200] C3 x C147 ---) [8, 3094, 2364409] C147
131) [2660869, 2757, 1235045] C3 x C147 ---) [5, 3301, 2660869] C147
132) [3307721, 1955, 128576] C3 x C147 ---) [41, 3910, 3307721] C147
133) [3413801, 1849, 1250] C3 x C147 ---) [8, 3698, 3413801] C147
134) [3626281, 1907, 2592] C3 x C147 ---) [8, 3814, 3626281] C147
135) [3646729, 1923, 12800] C3 x C147 ---) [8, 3846, 3646729] C147
136) [6638633, 2707, 172304] C3 x C147 5) [89, 5414, 6638633] C3 x C147
137) [6788777, 3155, 791312] C3 x C147 6) [137, 6310, 6788777] C3 x C147
138) [8008841, 3779, 1568000] C3 x C147 2) [5, 5737, 8008841] C3 x C147
139) [23812589, 7697, 8857805] C3 x C147 3) [5, 9781, 23812589] C3 x C147